# yI1-xI1.R
# Philips, Andrew Q. "How to Avoid Incorrect Inference (While Gaining Correct Ones) in Dynamic Models". Forthcoming at Political Science Research and Methods. 
# andrew.philips@colorado.edu
# 2/9/21
#
# Figures produced in this R script:
#   --Main Document, Figure 5: "yi1-xi1.pdf"
#   --SI, Figure 13: "yi1-xi1-evar5.pdf"
#   --SI, Figure 14: "yi1-xi1-mse-sr.pdf"
#   --SI, Figure 15: "yi1-xi1-mse-lr.pdf"
# -----------------------------------

rm(list = ls())
setwd("~/Dropbox/My_Folder/Papers-Projects/Wlezien-Enns-PSRM/Final-Feb2021/scripts/")
# -----------------------------------
library(dynamac)
library(nlWaldTest)
library(ggplot2)
library(grid)
library(gridExtra)
library(dplyr)

set.seed(8349809)
# -------------------------------------------------------------
# EXPERIMENT 3: Y ~ I(1), X ~ I(1)
sims = 2000 # no. sims
N <- c(50, 250, 1000) # number of obs
e.var <- c(1, 5) # error variance (in this case, variance in Y)

container.ardl <- matrix(NA, nrow = sims*length(N)*length(e.var), ncol = 9) # null matrix to hold output
# cols = sims, N, Beta.x, UL.beta.x, LL.beta.x, LR.x, LR.x.UL, LR.x.LL, e.var
container.ecm <- matrix(NA, nrow = sims*length(N)*length(e.var), ncol = 9) # null matrix to hold output
# cols = sims, N, Beta.x, UL.beta.x, LL.beta.x, LR.x, LR.x.UL, LR.x.LL, e.var
container.ldv <- matrix(NA, nrow = sims*length(N)*length(e.var), ncol = 9) # null matrix to hold output
# cols = sims, N, Beta.x, UL.beta.x, LL.beta.x, e.var
container.static <- matrix(NA, nrow = sims*length(N)*length(e.var), ncol = 6) # null matrix to hold output
# cols = sims, N, Beta.x, UL.beta.x, LL.beta.x, e.var
# -------------------------------------------------------------

row <- 1
prog <- txtProgressBar(min = 0, max = sims, style = 3)
for (s in 1:sims) {
    for (n in N) {
      for (ev in e.var) {
        setTxtProgressBar(prog, value = s)
        # create Y
        y <- cumsum(rnorm(n + 100, sd = sqrt(ev)))
        # create X
        x <- cumsum(rnorm(n + 100, sd = 1))
        # ARDL model:
        res.ardl <- lm(y[101:length(y)] ~ lshift(y, 1)[101:length(y)] + x[101:length(x)] + lshift(x, 1)[101:length(x)])
        # ECM model:
        res.ecm <- lm(dshift(y)[101:length(y)] ~ lshift(y, 1)[101:length(y)] + dshift(x)[101:length(x)] + lshift(x, 1)[101:length(x)])
        # LDV model
        res.ldv <- lm(y[101:length(y)] ~ lshift(y, 1)[101:length(y)] + x[101:length(x)])
        # static model
        res.static <- lm(y[101:length(y)] ~ x[101:length(x)])
      
        # grab QOI (FORALL): ----
        container.ardl[row, 1] <- container.ecm[row, 1] <- container.ldv[row, 1] <- container.static[row, 1] <- s
        container.ardl[row, 2] <- container.ecm[row, 2] <- container.ldv[row, 2] <- container.static[row, 2] <- n
        container.ardl[row, 9] <- container.ecm[row, 9] <- container.ldv[row, 9] <- container.static[row, 6] <- ev
      
        # QOI (ARDL)
        container.ardl[row, 3] <- coef(res.ardl)[3] # beta.x
        container.ardl[row, 4] <- confint.default(res.ardl, parm = c(3), level = 0.95)[2] # UL
        container.ardl[row, 5] <- confint.default(res.ardl, parm = c(3), level = 0.95)[1] # LL
        # LR effects (ARDL)
        lrm <- nlConfint(res.ardl, "(a[3] + a[4])/(1-a[2])", level = 0.95)
        container.ardl[row, 6] <- lrm[1] # LRM
        container.ardl[row, 7] <- lrm[3] # LRM UL
        container.ardl[row, 8] <- lrm[2] # LRM LL
      
        # QOI (ECM)
        container.ecm[row, 3] <- coef(res.ecm)[3] # beta.d.x
        container.ecm[row, 4] <- confint.default(res.ecm, parm = c(3), level = 0.95)[2] # UL
        container.ecm[row, 5] <- confint.default(res.ecm, parm = c(3), level = 0.95)[1] # LL
        # LR effects (ECM)
        lrm <- nlConfint(res.ecm, "(a[4])/(-a[2])", level = 0.95)
        container.ecm[row, 6] <- lrm[1] # LRM
        container.ecm[row, 7] <- lrm[3] # LRM UL
        container.ecm[row, 8] <- lrm[2] # LRM LL
      
        # QOI (LDV)
        container.ldv[row, 3] <- coef(res.ldv)[3]
        container.ldv[row, 4] <- confint.default(res.ldv, parm = c(3), level = 0.95)[2] # UL
        container.ldv[row, 5] <- confint.default(res.ldv, parm = c(3), level = 0.95)[1] # LL
        # LR effects (LDV)
        lrm <- nlConfint(res.ldv, "(a[3])/(1-a[2])", level = 0.95)
        container.ldv[row, 6] <- lrm[1] # LRM
        container.ldv[row, 7] <- lrm[3] # LRM UL
        container.ldv[row, 8] <- lrm[2] # LRM LL
      
        # QOI (static)
        container.static[row, 3] <- coef(res.static)[2]
        container.static[row, 4] <- confint.default(res.static, parm = c(2), level = 0.95)[2] # UL
        container.static[row, 5] <- confint.default(res.static, parm = c(2), level = 0.95)[1] # LL
      
        row <- row + 1
      } # close error var loop
    } # close N loop
} # close sim loop

#save.image("scenario-yi1-xi1-data.RData")
#load("scenario-yi1-xi1-data.RData")
head(container.ardl)
head(container.ecm)
head(container.ldv)
head(container.static)

# Create rejection rates and label:
container.ardl <- as.data.frame(container.ardl)
# cols = sim, N, Beta.x, UL.beta.x, LL.beta.x, LR.x, LR.x.UL, LR.x.LL, e.var
colnames(container.ardl) <- c("sims", "Time", "Beta.x", "Beta.x.ul", "Beta.x.ll", "LR.x", "LR.x.UL", "LR.x.LL", "e.var")
container.ecm <- as.data.frame(container.ecm)
# cols = sim, N, Beta.x, UL.beta.x, LL.beta.x, LR.x, LR.x.UL, LR.x.LL, e.var
colnames(container.ecm) <- c("sims", "Time", "Beta.x", "Beta.x.ul", "Beta.x.ll", "LR.x", "LR.x.UL", "LR.x.LL", "e.var")
container.ldv <- as.data.frame(container.ldv)
# cols = sim, N, Beta.x, UL.beta.x, LL.beta.x, LR.x, LR.x.UL, LR.x.LL, e.var
colnames(container.ldv) <- c("sims", "Time", "Beta.x", "Beta.x.ul", "Beta.x.ll", "LR.x", "LR.x.UL", "LR.x.LL", "e.var")
container.static <- as.data.frame(container.static)
# cols = sim, N, Beta.x, UL.beta.x, e.var
colnames(container.static) <- c("sims", "Time", "Beta.x", "Beta.x.ul", "Beta.x.ll", "e.var")

# proportion false rejection
container.ardl$reject.beta.x <- ifelse(container.ardl$Beta.x.ll > 0 | container.ardl$Beta.x.ul < 0, 1, 0)
container.ecm$reject.beta.x <- ifelse(container.ecm$Beta.x.ll > 0 | container.ecm$Beta.x.ul < 0, 1, 0)
container.ldv$reject.beta.x <- ifelse(container.ldv$Beta.x.ll > 0 | container.ldv$Beta.x.ul < 0, 1, 0)
container.static$reject.beta.x <- ifelse(container.static$Beta.x.ll > 0 | container.static$Beta.x.ul < 0, 1, 0)

# coverage of LRM:
container.ardl$reject.lrm <- ifelse(container.ardl$LR.x.LL > 0 | container.ardl$LR.x.UL < 0, 1, 0)
container.ecm$reject.lrm <- ifelse(container.ecm$LR.x.LL > 0 | container.ecm$LR.x.UL < 0, 1, 0)
container.ldv$reject.lrm <- ifelse(container.ldv$LR.x.LL > 0 | container.ldv$LR.x.UL < 0, 1, 0)

# squared error:
container.ardl$sqerr.beta <- (container.ardl$Beta.x - 0)^2
container.ecm$sqerr.beta <- (container.ecm$Beta.x - 0)^2
container.ldv$sqerr.beta <- (container.ldv$Beta.x - 0)^2
container.static$sqerr.beta <- (container.static$Beta.x - 0)^2
container.ardl$sqerr.lrm <- (container.ardl$LR.x - 0)^2
container.ecm$sqerr.lrm <- (container.ecm$LR.x - 0)^2
container.ldv$sqerr.lrm <- (container.ldv$LR.x - 0)^2

# collapse everything down:
container.collapse.ardl <- container.ardl %>%
  group_by(Time, e.var) %>%
  summarize(reject.beta.x = mean(reject.beta.x),
            reject.lrm = mean(reject.lrm),
            mse.beta = mean(sqerr.beta),
            mse.lrm = median(sqerr.lrm))

container.collapse.ecm <- container.ecm %>%
  group_by(Time, e.var) %>%
  summarize(reject.beta.x = mean(reject.beta.x),
            reject.lrm = mean(reject.lrm),
            mse.beta = mean(sqerr.beta),
            mse.lrm = median(sqerr.lrm))

container.collapse.ldv <- container.ldv %>%
  group_by(Time, e.var) %>%
  summarize(reject.beta.x = mean(reject.beta.x),
            reject.lrm = mean(reject.lrm),
            mse.beta = mean(sqerr.beta),
            mse.lrm = median(sqerr.lrm))

container.collapse.static <- container.static %>%
  group_by(Time, e.var) %>%
  summarize(reject.beta.x = mean(reject.beta.x),
            mse.beta = mean(sqerr.beta))

# combine all the model datasets since geom_bar doesn't work on separate datasets
container.collapse.ardl$model.type <- "ARDL"
container.collapse.ecm$model.type <- "ECM"
container.collapse.ldv$model.type <- "LDV"
container.collapse.static$model.type <- "Static"
# Create two appended datasets: 1 short run, 1 long run:
# short run: time, e.var, reject.beta.x, mse.beta, model.type
container.collapse.all.SR <- rbind(container.collapse.ardl[c(1,2,3,5,7)], container.collapse.ecm[c(1,2,3,5,7)], container.collapse.ldv[c(1,2,3,5,7)], container.collapse.static[c(1,2,3,4,5)])
# long run: time, e.var, reject.lrm, median square error, model type
container.collapse.all.LR <- rbind(container.collapse.ardl[c(1,2,4,6,7)], container.collapse.ecm[c(1,2,4,6,7)], container.collapse.ldv[c(1,2,4,6,7)])
container.collapse.all.LR$Time <- as.factor(container.collapse.all.LR$Time)
container.collapse.all.SR$Time <- as.factor(container.collapse.all.SR$Time)
container.collapse.all.LR$e.var <- as.factor(container.collapse.all.LR$e.var)
container.collapse.all.SR$e.var <- as.factor(container.collapse.all.SR$e.var)

# create a geom_bar when error variance = 1:
p1 <- ggplot(data = subset(container.collapse.all.SR, e.var == 1), aes(x = model.type, y = reject.beta.x, fill = Time)) + geom_bar(stat = "identity", position = position_dodge()) + theme_minimal() + scale_fill_brewer(palette="Oranges") + geom_hline(yintercept = 0.05, color = "black", size = 1)  + ylab("Proportion Rejected") + xlab("Model") + ggtitle("Short-Run") + scale_y_continuous(limits = c(0, 1))

p2 <- ggplot(data = subset(container.collapse.all.LR, e.var == 1), aes(x = model.type, y = reject.lrm, fill = Time)) + geom_bar(stat = "identity", position = position_dodge()) + theme_minimal() + scale_fill_brewer(palette="Oranges") + geom_hline(yintercept = 0.05, color = "black", size = 1) + ylab("Proportion Rejected") + xlab("Model") + ggtitle("Long-Run") + scale_y_continuous(limits = c(0, 1))

pdf("yi1-xi1.pdf", width = 1.618*7, height = 7)
grid.arrange(p1, p2, ncol = 2)
dev.off()

# error variance = 5:
p1 <- ggplot(data = subset(container.collapse.all.SR, e.var == 5), aes(x = model.type, y = reject.beta.x, fill = Time)) + geom_bar(stat = "identity", position = position_dodge()) + theme_minimal() + scale_fill_brewer(palette="Oranges") + geom_hline(yintercept = 0.05, color = "black", size = 1)  + ylab("Proportion Rejected") + xlab("Model") + ggtitle("Short-Run") + scale_y_continuous(limits = c(0, 1))

p2 <- ggplot(data = subset(container.collapse.all.LR, e.var == 5), aes(x = model.type, y = reject.lrm, fill = Time)) + geom_bar(stat = "identity", position = position_dodge()) + theme_minimal() + scale_fill_brewer(palette="Oranges") + geom_hline(yintercept = 0.05, color = "black", size = 1) + ylab("Proportion Rejected") + xlab("Model") + ggtitle("Long-Run") + scale_y_continuous(limits = c(0, 1))

pdf("yi1-xi1-evar5.pdf", width = 1.618*7, height = 7)
grid.arrange(p1, p2, ncol = 2)
dev.off()

# MSE across e.var and time, for SR:
p1 <- ggplot(data = subset(container.collapse.all.SR, e.var == 1), aes(x = model.type, y = mse.beta, fill = Time)) + geom_bar(stat = "identity", position = position_dodge()) + theme_minimal() + scale_fill_brewer(palette="Oranges") + ylab("Mean Square Error") + xlab("Model") + ggtitle("Variance = 1") + scale_y_continuous(limits = c(0, 2.25))

p2 <- ggplot(data = subset(container.collapse.all.SR, e.var == 5), aes(x = model.type, y = mse.beta, fill = Time)) + geom_bar(stat = "identity", position = position_dodge()) + theme_minimal() + scale_fill_brewer(palette="Oranges") + ylab("Mean Square Error") + xlab("Model") + ggtitle("Variance = 5") + scale_y_continuous(limits = c(0, 2.25))

pdf("yi1-xi1-mse-sr.pdf", width = 1.618*7, height = 7)
grid.arrange(p1, p2, ncol = 2)
dev.off()


# median square error across e.var and time, for LR:
p1 <- ggplot(data = subset(container.collapse.all.LR, e.var == 1), aes(x = model.type, y = mse.lrm, fill = Time)) + geom_bar(stat = "identity", position = position_dodge()) + theme_minimal() + scale_fill_brewer(palette="Oranges") + ylab("Median Square Error") + xlab("Model") + ggtitle("Variance = 1") + scale_y_continuous(limits = c(0, 2))

p2 <- ggplot(data = subset(container.collapse.all.LR, e.var == 5), aes(x = model.type, y = mse.lrm, fill = Time)) + geom_bar(stat = "identity", position = position_dodge()) + theme_minimal() + scale_fill_brewer(palette="Oranges") + ylab("Median Square Error") + xlab("Model") + ggtitle("Variance = 5") + scale_y_continuous(limits = c(0, 2))

pdf("yi1-xi1-mse-lr.pdf", width = 1.618*7, height = 7)
grid.arrange(p1, p2, ncol = 2)
dev.off()
